Volumes

Ok, quite a simple Question.

The base of a solid S is the region in the xy plane enclosed by the parabola y^2 = 4g and the line x=4, and each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis.

Show that the area of the semi ellipse at x=h is pi.h
(you may assume A = pi.ab)

The base of a solid S is the region in the xy plane enclosed by the parabola y^2 = 4g

I presume you mean [itex]y^2= 4x[/itex]

and the line x=4, and each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis.

Show that the area of the semi ellipse at x=h is pi.h
(you may assume A = pi.ab)

Ok, here's my question. Why is a = y and b = y/2. I dont get this

I assume you mean that a and b are the semi-axes of the ellipse. It would have been good to say that.

You are told that " each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis". The fact that the cross section is perpendicular to the x axis tells you that the measurement is semi-axis is parallel to the y-axis so its length is just "y". The fact that the other axis is 1/2 that tells you that its length is y/2.